PROCEEDINGS May 15, 16, 17, 18, 2005 - Casualty Actuarial Society

612 ESTIMATING THE WORKERS COMPENSATION TAILTABLE 3.5Indicated Paid Factors to UltimateEnd of Year of With 9% Without Ratio of 9% Inflation ReserveDevelopment Inflation Inflation to Zero Inflation Reserve10 2.684 1.152 11.115 2.469 1.110 13.425 2.019 1.054 18.935 1.594 1.022 27.050 1.192 1.003 64.0The paid factors to ultimate in the last column of Table 3.2above are exceptionally sensitive to future rates of claim inflation.Table 3.5 provides a comparison of the indicated tail factorswith and without inflation at various representative ages ofdevelopment.An example will put the implications of Table 3.5 into practicalterms. Suppose a claims adjuster reviews all PD claims openat the end of 25 years of development. For each PD claim, he estimatesthe medical portion by multiplying current medical paymentsby an annuity factor that is the life expectancy of theclaimant at his or her current age. The ratio of 18.9 in the rightcolumn of Table 3.5 is saying is that future medical paymentswill be 18.9 times the case reserve derived by this method. Onemight think that the error would decrease the more mature theaccident year became, but in actuality the percentage of error dramaticallyincreases at high maturities. In addition, the mortalitytable used by the claims adjuster may be out of date.Just as we have modeled the expected PLDF patterns for MPDlosses, analogous incurred loss development factor (ILDF) patternscan be estimated if we define total case reserves as theproduct of the latest year’s incremental payments times the averageannuity factor for all living PD claimants. This is presentedin Table 3.6.